NEW HAVEN — A city man suspected of fatally shooting a 28-year-old woman in her car two months ago was killed Wednesday in a shootout with Virginia state troopers, Police Chief Anthony Campbell said.

The Police Department, along with federal, state and local law enforcement,had spent June and July conducting a manhunt for Tramaine Marquese Poole, 42, after the slaying May 31 of Tyekqua Nesbitt.

While Virginia State Police have not positively identified the man as Poole, detectives from the New Haven Police Major Crimes Division left for Sussex County, Va., Wednesday morning, Officer David Hartman said in a news release. While Campbell said Poole had been killed, Hartman said the man “may be” Poole, but a positive identification had not been confirmed.

Upon learning the news, Tashauna Nesbitt, Tyekqua Nesbitt’s twin sister, said a rush of relief washed over her.

“I’m a little at ease. Now my niece and nephew can feel some kind of reassurance that they will be OK, that he’s gone. My mom can rest now, knowing that the person who took her daughter’s life away is gone,” Tashauna Nesbitt said of the suspect.

According to Sgt. Michelle Anaya of the Virginia State Police, the incident began at 8:18 a.m. when a vehicle, stolen out of Connecticut and traveling north on Interstate 95, refused to stop for a Virginia state trooper. A pursuit then ensued, with shots being fired from the pursued vehicle as it continued north on I-95 before taking an exit, the release said.

As the stolen vehicle approached an intersection, the pursuit suspect continued firing at the state police vehicles, with one of the bullets piercing a trooper’s back passenger window and striking and killing a state police dog that was riding in the backseat compartment, the release said.

Once the stolen vehicle was stopped, state troopers engaged with the suspect and shots were fired. The male suspect died at the scene and was to be taken to the office of the chief medical examiner in Richmond, Va., for examination and autopsy. A female passenger in the suspect vehicle was taken to a nearby hospital for treatment of nonlife-threatening injuries, the release said.

No troopers were injured . The investigation remains ongoing, the release said.

Tashauna Nesbitt said the past few months since her sister was slain have been one long nightmare.

“I’ve been pretty much up and down, all over the place,” she said.

Along with the consistent police presence for protection — “24 hours every day, everywhere we go,” she said — she has spent the time in constant fear.

“Every day, I would walk home to my house and make sure no one was around. He could [have] just come up any minute and killed someone else. Knowing that he’s not here to hurt anyone, I’m very much pleased,” Tashauna Nesbitt said.

While now, hopefully, she and her family, especially her niece and nephew, can get some semblance of their lives back, Poole’s death still doesn’t bring her sister back.

“It’s not going to bring my sister back. … Every day, I wake up missing my sister. I go to bed missing my sister,” she said.

Police found Nesbitt’s body in the area of Wilmot Road and Wintergreen Avenue when they were called to the area around 10:16 p.m. May 31. Her two children, ages 6 and 11, were in the car with her when she was shot, police said.

An arrest warrant was obtained, with $5 million bail to be imposed, charging Poole with murder, criminal possession of a firearm, carrying a pistol without a permit, two counts of risk of injury to a minor and unlawful discharge of a firearm, according to Assistant Chief Herb Johnson.

Campbell previously said law enforcement would search tirelessly until Poole was no longer on the streets of New Haven, or any city, where “he could continue to a be a threat to the very fabric of our society.”

“This is a dangerous individual. He has crossed all possible lines. Even in the criminal arena, he’s crossed the lines,” Campbell said previously.

U.S. Marshal for the District of Connecticut Brian Taylor said in July that the agency has been working with the Police Department following leads all over the country.

A $5,000 reward originally was offered by the U.S. Marshals’ Violent Fugitive Task Force, but State’s Attorney Pat Griffin asked on behalf of the Police Department for Gov. Dannel Malloy to approve $25,000 more. That request was granted, bringing the total reward to $30,000 for the arrest and conviction of Poole, Campbell said.

Officers initially were looking for Poole due to an active warrant for his arrest stemming from a domestic shooting May 7, but also were searching for him in connection with the May 31 slaying, as the two incidents are related and were being investigated as such.

In the May 7 incident, officers responded to the area outside Henry Street to investigate a reported shooting. The caller, a 36-year-old New Haven woman, called police as she was being driven to the hospital. She said she’d been shot by her husband on Henry Street. The city’s ShotSpotter system alerted police to the gunfire. The shooter was said to have been in a gray 2012 Audi.

The active arrest warrant for Poole in connection with the May 7 shooting charged him with first-degree assault, risk of injury, criminal possession of a firearm, carrying a pistol without a permit and unlawful discharge of a firearm, police said.

Poole had filed a restraining order against his wife just days before the domestic incident, requesting the court order her to stay away from him. In the restraining order, Poole wrote that he was concerned for his safety and about being set up, as his wife had allegedly threatened him in the past. He wrote that he wanted to protect himself, as he was allegedly “afraid of her temper,” court records show.

Court documents show the restraining order was dismissed as Poole failed to pick up the papers from the clerk’s office.